Algebra 2
posted by Peter on .
At a county fair, adults' tickets sold for $5.50, senior citizens' tickets for $4.00, and children's tickets for $1.50. On the opening day, the number of children's and senior's tickets sold was 30 more than half of the number of adults' tickets sold. the number senior citizens' tickets sold was 5 more than four times the number of children's tickets. How many of each type of ticket were sold if the total receipts from the ticket sales were $14, 970?

X = The # of adult tickets sold.
X/2 + 30 = The # of seniors & children
tickets sold.
5.5x + 5.5(x/2+30) = $14,970,
5.5x + 2.75x + 165 = 14,970,
8.25x + 165 = 14,970,
8.25x = 14,970  165 = 14,805,
X = 1795 Adult tickets sold.
x/2 + 30 = 1795/2 + 30 = 928 Children's
and seniors tickets sold.
Y = The # of children's tickets sold.
4y + 5 = The # of senior's tickets sold.
y + (4y+5) = 928,
5y + 5 = 928,
5y = 928  5 = 923,
Y = 185 Children's tickets sold.
4y + 5 = 4*185 + 5 = 745 Senior tickets